Well using it I just prooved it for the first column.
For the next columns, in the previews theorem I should know that for every x' != x
there is a y' != y. (!= is different)
Can anybody tell me whether this is true or not?
Also if it is, does anybody have any proof?
Yes there should be no loops.
Anyway
I read a theorem that may help. It says:
We have 2 trees T,T'.
For every edge (x) that belongs to T there is an edge (Y) that belongs to T' so that:
(T-{x})U{y} and (T'-{y})U{x} are also trees.
I'm trying to use it...
Graph problem!
Proove that:
If we have a matrix
|e11 e12 ... e1n|
|e21 e22 ... e2n|
| ..... |
|en1 en2 ... enn|
(eij edges of a graph G)
where every row is a spanning tree of G
then
there is a recomposition of every row so that the columns are also spanning trees of G.